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GCSE Maths · Practice Sheet 26

Sheet code: GCSE-MATHS-S26 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
An item is bought for £500 and sold for £700. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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2.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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3.
Quantitative Aptitude
The marked price of an item is £1,000. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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4.
Quantitative Aptitude
A can finish a job in 12 days and B in 4 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
Divide £689 between two people in the ratio 7:6. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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6.
Mathematics
In an arithmetic progression with first term 17 and common difference 7, find term number 13.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Quantitative Aptitude
Two varieties costing £39 and £97 per kg are mixed to give a mixture worth £69 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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8.
Mathematics
For the quadratic 1x² + 0x + 8 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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9.
Quantitative Aptitude
Find the simple interest on £33,000 at 5% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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10.
Quantitative Aptitude
The sum of the ages of two people is 83 years, and one is 3 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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11.
Quantitative Aptitude
Find the HCF and LCM of 36 and 38.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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12.
Mathematics
Evaluate ∫ from 1 to 3 of 1x^1 dx.
Formula:Definite Integral of a Power
$\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$
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13.
Mathematics
Find the sum of the first 5 terms of a GP with first term 6 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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14.
Quantitative Aptitude
The marked price of an item is £700. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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15.
Mathematics
If f(x) = 4x³ + 5x² + 6x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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16.
Mathematics
Evaluate ∫ from 0 to 4 of 5x^2 dx.
Formula:Definite Integral of a Power
$\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$
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17.
Quantitative Aptitude
A can finish a job in 4 days and B in 14 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
Find the simple interest on £40,000 at 12% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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19.
Quantitative Aptitude
A value changes from 200 to 240. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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20.
Quantitative Aptitude
Two varieties costing £34 and £66 per kg are mixed to give a mixture worth £53 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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